On Standardizing Within-Person Effects: Potential Problems of Global Standardization

Abstract

Person-mean centering has been recommended for disaggregating between-person and within-person effects when modeling time-varying predictors. Multilevel modeling textbooks recommended global standardization for standardizing fixed effects. An aim of this study is to evaluate whether and when person-mean centering followed by global standardization can accurately estimate fixed-effects within-person relations (the estimand of interest in this study) in multilevel modeling. We analytically derived that global standardization generally yields inconsistent (asymptotically biased) estimates for the estimand when between-person differences in within-person standard deviations exist and the average within-person relation is nonzero. Alternatively, a person-mean-SD standardization (P-S) approach yields consistent estimates. Our simulation results further revealed (1) how misleading the results from global standardization were under various circumstances and (2) the P-S approach had accurate estimates and satisfactory coverage rates of fixed-effects within-person relations when the number of occasions is 30 or more (in many conditions, performance was satisfactory with 10 or 20 occasions). A daily diary data example, focused on emotional complexity, was used to empirically illustrate the approaches. Researchers should choose standardization approaches based on theoretical considerations and should clearly describe the purpose and procedure of standardization in research articles.

Keywords:

• Within-person relations
• standardization
• multilevel modeling
• time-varying predictors

Conflict of Interest Disclosures

Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical Principles

The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Role of the Funders/Sponsors

None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments

The authors would like to thank the action editor Dr. Steve West and the anonymous reviewers for their helpful comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the author's institutions or the funding agency is not intended and should not be inferred.

Notes

1 Standardization also has limitations, which will be discussed later in the discussion section.

2 The online Supplemental materials can be downloaded from https://ldhrm.nd.edu/assets/289171/supplemental_materials_2018mbr.pdf.

3 P-S data cannot be obtained when the within-person sample SD is zero. In this case, we recommend that one can just person-mean center the data of the zero-WP-SD variable for the individual. This is because (1) the within-person sample covariance is 0 between this zero-WP-SD variable and another time-varying variable for the individual and (2) 0 times any weight is still 0.

4 Observed within-person SD, rather than latent WP SD, are used. So this approach is different from the approach in Schuurman et al. (2016).

5 Due to space limitations, we do not list the model forms with two or more time-varying predictors.

Additional information

Funding

Lijuan Wang was supported by NIH grants 1R21MH097675 and 1R01HD087319 from NIH when the research was conducted. The empirical data collection was supported by Grant 2 R01 AG02357-06 from NIA to C. S. Bergeman.